最 低 价：￥40.30
定 价：￥51.00
作 者：（美）Dale Varberg, Edwin J. Purcell, Steven E. Rigdon 著
出 版 社：机械工业出版社*
出版时间：2004 年1月
I S B N：7111107055
| 序. 出版说明 preface 1 preliminaries 1.1 the real number system 1.2 decimals,calculators,estimation 1.3 inequalities 1.4 absolute values,square roots,squares 1.5 the rectangular coordinate sytem 1.6 the straight line 1.7 graphs of equations 1.8 chapter erview technology project 1.1 graphing technology project 1.2 solving equations by xooming 2 functions and limits 2.1 functions and their graphs 2.2 operations on functions 2.3 the trigonometric functions 2.4 introduction to linits 2.5 rigorus study of limits .2.6 limit theorems 2.7 limits involving trigonometric functions 2.8 linits at infinity,infinite limits 2.9 continuity of functions 2.10 chapter review 2.11 additional problems technology project 2.1 shifting and scaling the graph of a function technology project 2.2 limits 3 the derivative 3.1 two problems with one theme 3.2 the derivative 3.3 rules for finding derivatives 3.4 derivatives of trigonometric functions 3.5 the chain rule 3.6 leibniz notation 3.7 higher-order derivatives 3.8 implicit differentiation 3.9 related rates 3.10 differentials and approximations 3.1 1 chapter review 3.12 additional problems technology project 3.1 secant and tangent lines technology project 3.2 linear approximation to a function 4 applications of the derivative 4.1 maxima and minima 4.2 monotonicity and concavity 4.3 local maxima and minima 4.4 more max-min problems 4.5 economic applications 4.6 sophisticated graphing 4.7 the mean value theorem 4.8 chapter review 4.9 additional problems technology project 4.1 reflection and refraction of light technology project 4.2 an optimization problem 5 the integral 5.1 antiderivatives (indefinite integrals) 5.2 introduction to differential equations 5.3 sums and sigma notation 5.4 introduction to area 5.5 the definite integral 5.6 the first fundamental theorem of calculus 5.7 the second fundamental theorem of calculus and the mean value theorem for integrals 5.8 evaluating definite integrals 5.9 chapter review 5.10 additional problems technology project 5.1 riemann sums technology project 5.2 accumulation functions 6 applications of the integral 6.1 the area of a plane region 6.2 volumes of solids: slabs, disks, washers 6.3 volumes of solids of revolution: shells 6.4 length of a plane curve 6.5 work 6.6 moments, center of mass 6.7 chapter review 6.8 additional problems technology project 6.1 volume in an elliptical cylinder technology project 6.2 arc length 7 transcendental functions 7.1 the natural logarithm function 7.2 inverse functions and their derivatives 7.3 the natural exponential function 7.4 general exponential and logarithmic functions 7.5 exponential growth and decay 7.6 first-order linear differential equations 7.7 the inverse trigonometric functions and their derivatives 7.8 the hyperbolic functions and their inverses 7.9 chapter review 7.10 additional problems technology project 7.1 special functions technology project 7.2 population growth and least squares 8 techniques of integration 8.1 integration by substitution 8.2 some trigonometric integrals 8.3 rationalizing substitutions 8.4 integration by parts 8.5 integration of rational functions 8.6 chapter review technology project 8.1 integration using a computer algebra system technology project 8.2 the logistic differential equation 9 indeterminate forms and improper integrals 9.1 indeterminate forms of type 0/0 9.2 other indeterminate forms 9.3 improper integrals: infinite limits of integration 9.4 improper integrals: infinite integrands 9.5 chapter review 9.6 additional problems technology project 9.1 probability density functions technology project 9.2 the normal distribution 10 infinite series 10.1 infinite sequences 10.2 infinite series 10.3 positive series: the integral test 10.4 positive series: other tests 10.5 alternating series, absolute convergence, and conditional convergence .. 10.6 power series 10.7 operations on power series 10.8 taylor and maclaurin series 10.9 chapter review technology project 10.1 using infinite series to approximate technology project 10.2 euler's derivation 11 numerical methods, approximations 11.1 the taylor approximation to a function 11.2 numerical integration 11.3 solving equations numerically 11.4 the fixed-point algorithm 11.5 approximations for differential equations 11.6 chapter review technology project 11.1 maclaurin polynomials technology project 11.2 numerical integration technology project 11.3 bisection, newton's, and fixed-point methods 12 conics and polar coordinates 12.1 the parabola 12.2 ellipses and hyperbolas 12.3 more on ellipses and hyperbolas 12.4 translation of axes 12.5 rotation of axes 12.6 the polar coordinate system 12.7 graphs of polar equations 12.8 calculus in polar coordinates 12.9 chapter review technology project 12.1 rotations in the plane technology project 12.2 another kind of rose 13 geometry in the plane, vectors 13.1 plane curves: parametric representation 13.2 vectors in the plane: geometric approach 13.3 vectors in the plane: algebraic approach 13.4 vector-valued functions and curvilinear motion 13.5 curvature and acceleration 13.6 chapter review technology project 13.1 hypocycloids technology project 13.2 measuring home run distance 14 geometry in space, vectors 14.1 cartesian coordinates in three-space 14.2 vectors in three-space 14.3 the cross product 14.4 lines and curves in three-space 14.5 velocity, acceleration, and curvature 14.6 surfaces in three-space 14.7 cylindrical and spherical coordinates 14.8 chapter review technology project 14.1 curves in three-space technology project 14.2 the ferris wheel and the corkscrew roller coaster 15 the derivative in n-space 15.1 functions of two or more variables 15.2 partial derivatives 15.3 limits and continuity 15.4 differentiability 15.5 directional derivatives and gradients 15.6 the chain rule 15.7 tangent planes, approximations 15.8 maxima and minima 15.9 lagrange's method 15.10 chapter review technology project 15.1 newton's method for two equations in two unknowns technology project 15.2 visualizing the directional derivative 1 6 the integral in n-space 16.1 double integrals over rectangles 16.2 iterated integrals 16.3 double integrals over nonrectangular regions 16.4 double integrals in polar coordinates 16.5 applications of double integrals 16.6 surface area 16.7 triple integrals (cartesian coordinates) 16.8 triple integrals (cylindrical and spherical coordinates) 16.9 chapter review technology project 16.1 newton's law of gravitation technology project 16.2 monte carlo integration 17 vector calculus 17.1 vector fields 17.2 line integrals 17.3 independence of path 17.4 green's theorem in the plane 17.5 surface integrals 17.6 gauss's divergence theorem 17.7 stokes's theorem 17.8 chapter review technology project 17.1 line integrals and work technology project 17.2 parametrized surfaces 18 differential equations 18.1 linear homogeneous equations 18.2 nonhomogeneous equations 18.3 applications of second-order equations 18.4 chapter review 786 technology project 18.1 vibrating spring technology project 18.2 phase portraits appendix a. 1 mathematical induction a.2 proofs of several theorems a.3 a backward look answers to odd-numbered problems index photo credits ... |
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